In Breaking Bad, Mike clearly calls Jimmy by his alternate name "Saul" multiple times. In Better Call Saul, we see that their paths are crossed quite considerably before Jimmy even starts using his alter ego of Saul Goodman.
Why does Mike entertain this alter ego name? He doesn't seem to be the type of guy who would do so, regardless of Jimmy's reasons for using it. It seems to be a bit of a plot hole (granted, it isn't a big one). I can see why someone would disagree with me on this point, but Gilligan's style is so careful and thought-out that it's surprising that something like this would be left unturned. Concepts of Better Call Saul were thought of well before Breaking Bad had finished airing, so I would've thought they had plenty of time to close any of these holes.